In order to be differentiable everywhere, 
must first be continuous everywhere, which means the limits from either side as 
must be the same and equal to 
. By definition, 
, and
so we need to have 
.
For to be differentiable at 
, the derivative needs to be continuous at , i.e.
We then need to have
Then
Answer:
Solution of a System. In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.
Answer:
3.5132719e+24
Step-by-step explanation:
Answer: 0.16
Step-by-step explanation:
Given that the run times provided are normally distributed ;
Mean(x) of distribution = 3 hours 50 minutes
Standard deviation(s) = 30 minutes
The probability that a randomly selected runner has a time less than or equal to 3 hours 20 minutes
3 hours 20 minutes = (3 hrs 50 mins - 30 mins):
This is equivalent to :
[mean(x) - 1 standard deviation]
z 1 standard deviation within the mean = 0.84
z, 1 standard deviation outside the mean equals:
P(1 - z value , 1standard deviation within the mean)
1 - 0.8413 = 0.1587
= 0.16
Answer:
Step-by-step explanation:
Hello
To simplify the polynomial we must eliminate the parentheses
by definition
I hope it helps
Have a great day
